Related papers: Geometry of some twistor spaces of algebraic dimen…

We show that the algebraic dimension of a twistor space over n#CP^2 cannot be two if n>4 and the fundamental system (i.e. the linear system associated to the half-anti-canonical bundle, which is available on any twistor space) is a pencil.…

Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarized K3 surface with complex multiplication, all…

A study is made of algebraic curves and surfaces in the flag manifold $\mathbb{F}=SU(3)/T^2$, and their configuration relative to the twistor projection $\pi$ from $\mathbb{F}$ to the complex projective plane $\mathbb{CP}^2$, defined with…

We exploit techniques from classical (real and complex) algebraic geometry for the study of the standard twistor fibration $\pi:\mathbb{CP}^{3}\to S^{4}$. We prove three results about the topology of the twistor discriminant locus of an…

We study the algebraic dimension of twistor spaces of positive type over $4\bbfP^2$. We show that such a twistor space is Moishezon if and only if its anticanonical class is not nef. More precisely, we show the equivalence of being…

We prove that a reduced and irreducible algebraic surface in $\mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalization map of a…

We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce's self-dual metrics on the 4-manifold H^2 x T^2 that extend smoothly to nCP^2, the connected sum of complex projective planes. Indeed, we explicitly realize…

We continue to study twistor spaces on the connected sum of four complex projective planes, whose anticanonical map is of degree two over the image. In particular, we determine the defining equation of the branch divisor of the…

We deal here with the geometry of the twistor fibration $\mathcal{Z} \to \bb{S}^3_1$ over the De Sitter 3-space. The total space $\mathcal{Z}$ is a five dimensional reductive homogeneous space with two canonical invariant almost CR…

In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon…

It is very well known that Hopf real hypersurfaces in the complex projective space can be locally characterized as tubes over complex submanifolds. This also holds true for some, but not all, Hopf real hypersurfaces in the complex…

A very basic introduction is given to the r\^oles of division algebras and the related sphere algebras concerning the structure of space-time in the dimensionalities $D\is 3,4,6$ and $10$, with special emphasis on twistors transformations…

As an application of the method of [4], we find the metric and connection on the space of conics in $\mathbb{CP}^2$ determined as the solution space of the ODE eqn(1). These calculations underpin the twistor construction of the Radon…

It is shown that there exist non-singular cubic surfaces in CP^3 containing 5 twistor lines. This is the maximum number of twistor fibres that a non-singular cubic can contain. Cubic surfaces in CP^3 with 5 twistor lines are classified up…

In this paper we explicitly construct Moishezon twistor spaces on nCP^2 for arbitrary n>1 which admit a holomorphic C*-action. When n=2, they coincide with Y. Poon's twistor spaces. When n=3, they coincide with the one studied by the author…

Let $X$ be a quasi-projective curve, compactified to $(Y,D)$ with $X=Y-D$. We construct a Deligne-Hitchin twistor space out of moduli spaces of framed $\lambda$-connections of rank $2$ over $Y$ with logarithmic singularities and…

We describe complex twistor spaces over inner 3-symmetric spaces $G/H$, such that $H$ acts transitively on the fibre. Like in the symmetric case, these are flag manifolds $G/K$ where $K$ is the centralizer of a torus in $G$. Moreover, they…

We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear…

For an algebraic K3 surface with complex multiplication (CM), algebraic fibres of the associated twistor space away from the equator are again of CM type. In this paper, we show that algebraic fibres corresponding to points at the same…

In this paper we investigate a family of Moishezon twistor spaces on the connected sum of 4 complex projective planes, which can be regarded as a direct generalization of the twistor spaces on 3CP^2 of double solid type studied by Poon and…